Download App

STD 11- 2. Relation and Function — Maths STD 11 Science — Question

CBSE BoardEnglish MediumSTD 11 ScienceMathsSTD 11- 2. Relation and Function1 Mark
MCQ
Domain of the function $f(x) = \sqrt {2 - 2x - {x^2}} $ is
  • A
    $ - \sqrt 3 \le x \le \sqrt 3 $
  • ✓
    $ - 1 - \sqrt 3 \le x \le - 1 + \sqrt 3 $
  • C
    $ - 2 \le x \le 2$
  • D
    $ - 2 + \sqrt 3 \le x \le - 2 - \sqrt 3 $
✓

Answer

Correct option: B.
$ - 1 - \sqrt 3 \le x \le - 1 + \sqrt 3 $
b
(b) The quantity under root is positive, when

If we want the range of $f(x)$ to be real then, $0 \leq 2-2 x-x^{2}$

$\Longrightarrow x^{2}+2 x \leq 2$

$\Longrightarrow x^{2}+2 x+1 \leq 3$

$\Longrightarrow(x+1)^{2} \leq 3$

$\Longrightarrow-\sqrt{3} \leq x+1 \leq \sqrt{3}$

$\Longrightarrow-\sqrt{3}-1 \leq x \leq \sqrt{3}-1$

So the domain of $x$ is $[-1-\sqrt{3},-1+\sqrt{3}]$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "M.C.Q (1 Marks)" from STD 11- 2. Relation and Function→STD 11- 2. Relation and Function — all question types→Maths STD 11 Science question papers→CBSE Board STD 11 Science question papers→CBSE Board question paper generator→

Similar questions

In a class of $100$ students,$15$ students chose only physics (but not mathematics and chemistry),$3$ chose only chemistry (but not mathematics and physics), and $45$ chose only mathematics(but not physics and chemistry). Of the remaining students, it is found that $23$ have taken physics and chemistry,$20$ have taken physics and mathematics, and $12$ have taken mathematics and chemistry. The number of student who chose all the three subjects is
→
Circle$(s)$ touching $x$-axis at a distance $3$ from the origin and having an intercept of length $2 \sqrt{7}$ on $y$-axis is (are)

$(A)$ $x^2+y^2-6 x+8 y+9=0$

$(B)$ $x^2+y^2-6 x+7 y+9=0$

$(C)$ $x^2+y^2-6 x-8 y+9=0$

$(D)$ $x^2+y^2-6 x-7 y+9=0$

→
$\cos 1^\circ + \cos 2^\circ + \cos 3^\circ + ..... + \cos 180^\circ = $
→
Let the six numbers $a_1, a_2, a_3, a_4, a_5, a_6$ be in $A.P.$ and $a_1+a_3=10$. If the mean of these six numbers is $\frac{19}{2}$ and their variance is $\sigma^2$, then $8 \sigma^2$ is equal to
→
If $\text{f(x)}=64\text{x}^3+\frac{1}{\text{x}^3}$ and $\alpha,\beta$ are the roots of $4\text{x}+\frac{1}{\text{x}}=3.$ Then,
→
If $\omega $ is non real root of equation $x^3 - 1 = 0$, then value of $\sum\limits_{r = 1}^5 {\left( {1 + {\omega ^r} + {\omega ^{2r}}} \right)} $ is
→
Total number of words formed by $2$ vowels and $3$ consonants taken from $4$ vowels and $5$ consonants is equal to.
→
If ${z_1}$ and ${z_2}$ are two non-zero complex numbers such that $|{z_1} + {z_2}| = |{z_1}| + |{z_2}|,$then arg $({z_1}) - $arg $({z_2})$ is equal to
→
Let $A\,(4, -4)$ and $B\,(9,6)$ be points on the parabola $y^2 = 4x$ . Let $C$ be chosen on the arc $AOB$ of the parabola, where $O$ is the origin, such that the area of $\Delta ACB$ is maximum. Then, the area (in sq. units) of $\Delta ACB,$ is
→
If the point of intersections of the ellipse $\frac{ x ^{2}}{16}+\frac{ y ^{2}}{ b ^{2}}=1$ and the circle $x ^{2}+ y ^{2}=4 b , b > 4$ lie on the curve $y^{2}=3 x^{2},$ then $b$ is equal to:
→